A leak in the tank — Time & Work Aptitude Question
A leak in the tank: A tap fills a tank in 6 hours. A leak at the bottom empties a full tank in 12 hours. Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 45 seconds
Question
A tap fills a tank in 6 hours. A leak at the bottom empties a full tank in 12 hours. With both working, how long does the tank take to fill?
Options
- 9 h
- 10 h
- 12 h
- 18 h
Show the answer and the worked solution
Correct answer: C. 12 h
Worked solution
- Net rate = 1/6 − 1/12 = 2/12 − 1/12 = 1/12.
- The tank fills in 12 hours.
Answer: 12 h.
The idea
The leak halves the effective rate here, so the time doubles. Subtracting the times (12 − 6) would give 6 and is wrong.
Shortcut. Filler against leak: time = product ÷ difference = 6 × 12 ÷ (12 − 6) = 12 hours.
Common trap. 18 h — adding the two times (6 + 12); the leak removes half the tap's rate, which doubles 6 hours to 12.